[Groxx]

They block you from doing this if you're not logged in (as I discovered after wiping and rooting one to give to a friend recently).

As evidence, note that instructions for rooting them requires the device to be registered - this is because it won't be accessible over USB until you do so: https://kindlemodding.org/jailbreaking/WinterBreak/

So if you can't log in...

[pjmlp]

Not a thing on my e-ink kindle, although it is a decade old by now.